The new House GOP leaders who were made to pull back border legislation Thursday reached out to disgruntled tea party conservatives, tamping down the rebellion on the right but making a deal with the Senate even more unlikely.

Speaker of the House John Boehner (R) of Ohio is surrounded by reporters on Capitol Hill in Washington, after a closed-door meeting of House Republicans to discuss the border crisis on Friday. GOP leaders expressed optimism that a revised bill to address the surge of immigrants over the US-Mexico border would win over reluctant conservatives and give a divided GOP a political win.

WASHINGTON — It looks as if the new GOP leadership team in the House may redeem itself later Friday when it plans to offer – for a second time – legislation to address the child-migrant crisis on the border.

On Thursday, acrimony and chaos ruled as House Speaker Boehner (R) of Ohio and the new majority leader, Rep. Kevin McCarthy (R) of California, were forced by a conservative rebellion to pull two border-related bills from the floor. The votes, corralled by the new whip, Rep. Steve Scalise (R) of Louisiana, fell short.

It was a disastrous first official day on the job for the leadership trio, reconfigured after then-majority leader Eric Cantor lost his Virginia primary race in an upset June 10. On Thursday, fingers pointed at Congressman Scalise, because he had been elected to his vote-counting post specifically to represent Southern, hard-line conservatives – of which he is one. With Scalise on the team, the party was supposed to be more unified.

Instead, the leadership faced an embarrassing debacle on the floor, followed by a contentious closed-door meeting with Republican members. But then Rep. Raul Labrador, a conservative from Idaho whom Scalise had asked for help because of his immigration expertise, gathered together the 20 or so “no” votes in a House basement conference room. Over the course of about two hours, he heard out the contrarians, while a staff member from the leadership team translated their suggestions into legislative language. Scalise also dropped by.

By Friday morning, several of the leadership’s harshest critics were all smiles.

“What happened between last night and this morning is absolutely remarkable,” said Rep. Michele Bachmann of Minnesota, a tea-party darling and former presidential candidate.

“We got to ‘yes’ very fast. It wasn’t contentious. There were no fisticuffs. There were no blows. We did this very civilly,” she said before cameras on Friday.

“It’s like I ordered it off the menu,” Rep. Steve King (R) of Iowa, told Roll Call, speaking of the changes to the bills.

“This looks like a new dawn for the way we’re going to handle problems,” said Rep. Matt Salmon (R) of Arizona. “Instead of trying to push people in the right direction, [the leadership] is trying to win the hearts and the minds of people and let them actually have a say when they have a disagreement.”

All three had met Wednesday with Sen. Ted Cruz, the tea party freshman from Texas who is considering a presidential run in 2016. Much criticized for interfering with House business, Senator Cruz has expressed his dismay over the original House bill because it doesn’t end “amnesty” – President Obama’s 2012 executive action to defer deportation for certain children of illegal immigrants, known as the Deferred Action for Childhood Arrivals program, or DACA.

In answer to conservatives’ complaints, the new legislation will, among other things, spend $35 million more to deploy National Guard troops to the border, bringing the total cost to $694 million – covered by offsets and still a far cry from the president’s request of $3.7 billion. It changes language related to the deportation and adjudication of minors. And a separate bill is reportedly being toughened to prevent extending DACA beyond its current two-year period.

Some Republicans still question whether the leadership has the votes even for these bills – moderates might peel off, for instance. But this morning, several Republicans on the more moderate side said they would vote for the bills, and also praised the leadership’s outreach.

“I didn’t support Scalise for whip,” said Rep. Richard Hudson (R) of North Carolina. But, he said, “I as well as a lot of people really appreciated the process” of collecting feedback and acting on it. “It’s been a little painful,” he admitted. “Making sausage is always ugly.”

Here’s the thing though. Let’s say this new team manages to keep the tea party at a simmer instead of a boil. It will do so by precisely this kind of action – by being more accommodating to tea party views. That means a continued drift to the right.

And as a result, House-passed bills will continue to pile up in the Senate trash can – with the immediate consequence that the child-migrant crisis is still in search of a solution (especially since the Senate failed to pass its own bill Thursday).

The House leadership “might have a bill today but it is only by caving to the most extreme voices of their party – capitulating rather than leading – which won't bring them legislation down the road that the president will sign or which Democrats will accept,” writes Julian Zelizer, a congressional historian at Princeton University, in an e-mail.

“At some point, if the GOP wants to rebuild their party, they will need to find ways to contain the tea party rather than having them run the show.”